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Geometric constructions have been a popular part of mathematics throughout history. The first chapter here is informal and starts from scratch, introducing all the geometric constructions from high school that have been forgotten or were never learned. The second chapter formalises Plato's game, and examines problems from antiquity such as the impossibility of trisecting an arbitrary angle. After that, variations on Plato's theme are explored: using only a ruler, a compass, toothpicks, a ruler and dividers, a marked rule, or a tomahawk, ending in a chapter on geometric constructions by paperfolding. The author writes in a charming style and nicely intersperses history and philosophy within the mathematics, teaching a little geometry and a little algebra along the way. This is as much an algebra book as it is a geometry book, yet since all the algebra and geometry needed is developed within the text, very little mathematical background is required. This text has been class tested for several semesters with a master's level class for secondary teachers.
On the basis of synchronic and diachronic data analysis, the volume takes a close look at the synchronic layers of binominal size noun and type noun uses (a bunch/a load of X; a sort of X; a Y type of X) and reconsiders the framework of grammaticalization in view of issues raised by the phrases under discussion. As a result, a construction grammar-approach to grammaticalization is developed which does justice to the syntagmatic lexical, or collocational, reclustering observed in the data within an eclectic cognitive-functional approach.